Question

# Four students reported their study time and test score from a statistics course and their data...

Four students reported their study time and test score from a statistics course and their data have been converted into Z scores in the table below. What is Pearson's correlation coefficient from this data set?

a.)-.50

b.)-.25

c.).75

d.)-1.00

In what situation would a researcher use a  t-test used instead of a Z-test?

a.)When there is only one sample.

b.)When the population standard deviation is unknown.

c.)When the sample size is smaller than 30.

d.)When the population is normally distributed.

If you conduct a two-tailed test at the .05 level of significance, with a degree of freedom of 30, what would be your critical t score on the t distribution?

a.)±2.043

b.)±1.729

c.)2.043

d.)1.729

A researcher tested a research hypothesis that people with diagnosed depression will have REDUCED level of depressive symptoms after a cognitive therapy treatment, as compared to the pre-treatment level of depressive symptoms. The cutoff t value is -1.746 for this one-tailed test. The data analysis yielded a mean change score (post-treatment minus pre-treatment) of -3. If the standard error is 2.0, what is the t statistic and what is the conclusion of the hypothesis test?

a.)-1.50; fail to reject the null hypothesis

b.)-1.50; reject the null hypothesis

c.)-1.25; fail to reject the null hypothesis

d.)-1.25; reject the null hypothesis

1)Since study time and test scores are directly related to each other ( as study time increases test scores also increase) the correlation coefficient will be positive value.

r = 0.75

Negative scores indicate inverse relationship.

2) t test and z assume that population should be normally distributed and both can be used to test single population mean .

Z test assumes that population standard deviation is known.

Correct option : when population standard deviation is unknown.

3) critical value of t for two sided test at df 30 is equal to +- 2.043. When test is two sided it's critical region is equally divided on two sides of distribution. Therefore there are two critical values . Positive critical values are only for right tailed test.

4) t = mean change score/ standard Error

t = -3/2 = - 1.5

| - 1.746 | > | -1.5 | , we fail to Reject Null hypothesis.

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